Question: If $x$ is doubled, increased by $3$, and then divided by $5$, the result is $11$. What is the value of $x$?
We set up the equation and solve for $x$: \begin{align*}
\frac{2x+3}{5}&=11\qquad\Rightarrow\\
2x+3&=55\qquad\Rightarrow\\
2x&=52\qquad\Rightarrow\\
x&=\boxed{26}.
\end{align*}